Sandra deposits $3,000 at the beginning of each semiannual period for 12 years at 10% interest compounded semiannually. Determine the amount she will have in the account after 12 years. Round to the nearest cent.

a.

$130,506.00

c.

$121,291.43

b.

$140,181.30

d.

$70,568.14

Annuity formula for depositing at the end of each period.

Future value,

F=A * ((1+i) ^n-1) / i

A=deposit per period, $3000

i=interest per period, 10%/2 = 5% = 0.05 per half year

n=number of periods = 12 years = 24 half-years

If the deposit is at the beginning of each period, then

we can use the above formula, with 25 periods, but skipping the final payment, i. e.

F=A * ((1+i) ^ (n+1) - 1) / i-A

=3000 * ((1+.1/2) ^ (24+1) - 1) / (.1/2) - 3000

=143181.296 - 3000

=143181.30 - 3000

=140181.30 (to the nearest cent)